1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Salsk061 [2.6K]
3 years ago
12

Question 1 (13 marks) A charge Q is located on the top-left corner of a square. Charges of 2Q, 3Q and 4Q are located on the othe

r corners as shown above in the Figure. Assuming each side of the square is 5cm in length, and the charge Q= 2.5 µC, determine the net force exerted on the 2Q charge due to the other charges.

Physics
1 answer:
tino4ka555 [31]3 years ago
3 0

Answer:

F = 45 (2.4142 i ^ + 4.414 j ^)

  F = 226.40 N,           θ= 61.3

Explanation:

For this exercise we will use that the forces are vectors and we will add them, the force due to being electric charges must comply, go Coulomb's law

         F₁₂ = k q₁ q₂ / r₁₂²

To apply this equation to our case, they indicate that all charges are of the same sign and their value, also the charge Q is located in the upper left corner, unfortunately the diagram of the other charges is not loaded, but the most general is that is in sequence, see attached, for the sum of the forces let's add its components

x-axis (horizontal)

         Fₓ = F₂₁ + F₂₄ₓ

Let's use trigonometry for the force component, as the weathering figure is a square the angle between the force and the x axis is 45

        cos 45 = F₂₄ₓ / F₂₄

         F₂₄ₓ = F₂₄ cos 45

y-axis (vertical)

        F_{y} = F₂₃ + F_{24y}

        sin 45 = F_{24y} / F₂₄

        F_{24y} = F₂₄ sin 45

let's search every distance

The side of the square is worth l = 5cm = 0.05 m

we can find the diagonal with the Pythagorean theorem

         d = √(l² + l²) = l √2

now we can search every force

         F₂₁ = k q₁ q₂ / r₁₂²

         F₂₁ = k Q 2Q / l²

         F₂₁ = k 2Q² / l²

this force points in the positive x direction

         F₂₃ = k q₂ q₃ / r₂₃²

         F₂₃ = k 2Q 3Q / l²

this force points in the direction of the positive y

         F₂₄ = k q₄q₂ / d²

         F₂₄ = k 4Q 2Q / 2 l²

let's find the resultant in each x

X axis

        Fₓ = k 2Q² / l² + k 8Q² / 2 l²    cos 45

        Fₓ = k 2Q² / l² (1 + 4/2 cos 45)

        Fₓ = k 2Q²/ l²   2.4142 i ^

Axis y

       F_{y} = k 6Q² / l² + k 8Q² / 2 l²    sin 45

       F_{y} = k 2Q² / l² (3 + 4/2 sin45)

       F_{y} = k 2Q² / l² (4,414)

       

the resultant force

       F = Fₓ i ^ + F_{y} j ^

       F = k 2Q² / l²      ( 2.4142 i ^ + 4.414 j ^)

       

let's substitute the values

       F = 9 10⁹ 2 (2.5 10⁻⁶) 2 / 0.05²      (2.4142 i ^ + 4.414 j ^)

       F = 45 (2.4142 i ^ + 4.414 j ^)

The result we can give is this form and in the form of module and angle

             

let's use the Pythagorean theorem to find the modulus

            F =√ (Fₓ² +  F_{y}²)

            F = 45 √ (2.4142² + 4.414²)

            F = 226.40 N

we use trigonometry for the angle, measured from the x-axis

           tan θθ = Fy / Fx

          θ  = tan⁻¹ (4.414 / 2.4142)

           θ= 61.3

You might be interested in
WHY IS SATURN ONE OF THE COLDEST PLANETS IN OUR SOLAR SYSTEM
Usimov [2.4K]
What are the answer choices?
4 0
3 years ago
What are the only elements that exist in nature as isolated atoms
agasfer [191]

Answer:

The only such elements are the Noble Gases (He, Ne, Ar, Kr, Xe, Rn)

(that is helium, neon, argon, krypton, xenon and radon)

Term: Monoatomic

Explanation:

6 0
3 years ago
When the mass of the bottle is 0.125 kg, the KE is______ kg m2/s2.
DiKsa [7]
Answers are:
(1) KE = 1 kg m^2/s^2
(2) KE = 2 kg m^2/s^2
(3) KE = 3 kg m^2/s^2
(4) KE = 4 kg m^2/s^2


Explanation:

(1) Given mass = 0.125 kg
speed = 4 m/s

Since Kinetic energy = (1/2)*m*(v^2)

Plug in the values:
Hence:
KE = (1/2) * 0.125 * (16)
KE = 1 kg m^2/s^2

(2) Given mass = 0.250 kg
speed = 4 m/s

Since Kinetic energy = (1/2)*m*(v^2)

Plug in the values:
Hence:
KE = (1/2) * 0.250 * (16)
KE = 2 kg m^2/s^2

(3) Given mass = 0.375 kg
speed = 4 m/s

Since Kinetic energy = (1/2)*m*(v^2)

Plug in the values:
Hence:
KE = (1/2) * 0.375 * (16)
KE = 3 kg m^2/s^2

(4) Given mass = 0.500 kg
speed = 4 m/s

Since Kinetic energy = (1/2)*m*(v^2)

Plug in the values:
Hence:
KE = (1/2) * 0.5 * (16)
KE = 4 kg m^2/s^2
3 0
3 years ago
Which groups of organisms became extinct during the Paleozoic Era
guapka [62]
Dinosaurs but I need the whole groups yo tell you ;)
4 0
3 years ago
How do I calculate initial speed by using the slope of a graph? The graph shows the relationship between S {(sin2ϴ)/g} and the a
Orlov [11]
The formula for slope is y=mx+b
3 0
3 years ago
Other questions:
  • During the expansion of the early universe, which two interactions were the last to separate? a. the strong and weak interaction
    12·1 answer
  • A force of 99 N causes a box to accelerate at a rate of 11 m/s2. What is the mass of the box? (Ignore frictional effects.) 1,100
    8·2 answers
  • Isotopes of uranium have the same number of ________ but a different number of _________.
    14·2 answers
  • Stars originate as large bodies of slowly rotating gas.Because of gravity, these clumps of gas slowly decrease in size.The angul
    6·1 answer
  • 3. What is the relationship among wave speed, wavelength, and frequency?
    8·1 answer
  • Three biological applications of electricity
    15·1 answer
  • Complete the wording of the Law of Conservation of Matter and Energy (as defined in the text).
    11·1 answer
  • The derived unit for pressure​
    7·2 answers
  • How do meteorologists gather data
    13·1 answer
  • the aeroplane in fig 3.1 flies an outward journey from Budapest (Hungary) to palermo (Italy) in 2.75 the distance is 2200 KM (i)
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!